Quantum-Assisted Trainable-Embedding Physics-Informed Neural Networks for Parabolic PDEs

• URL: http://arxiv.org/abs/2602.14596v1
• Date: Mon, 16 Feb 2026 09:59:01 GMT
• Title: Quantum-Assisted Trainable-Embedding Physics-Informed Neural Networks for Parabolic PDEs
• Authors: Ban Q. Tran, Nahid Binandeh Dehaghani, Rafal Wisniewski, Susan Mengel, A. Pedro Aguiar,
• Abstract summary: Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs)<n>Recent advances in quantum machine learning have motivated hybrid quantum-classical extensions aimed at enhancing representational capacity.<n>In this work, we investigate trainable embedding strategies within quantum-assisted PINNs for solving parabolic PDEs.
• Score: 1.7887197093662073
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding governing physical laws directly into the training objective. Recent advances in quantum machine learning have motivated hybrid quantum-classical extensions aimed at enhancing representational capacity while remaining compatible with near-term quantum hardware. In this work, we investigate trainable embedding strategies within quantum-assisted PINNs for solving parabolic PDEs, using one- and two-dimensional heat equations as canonical benchmarks. We introduce two quantum-assisted architectures that differ in their embedding components. In the first approach, a classical feed-forward neural network generates trainable feature maps for quantum data encoding (FNN-TE-QPINN). In the second, the embedding stage is realized entirely by a parameterized quantum circuit (QNN-TE-QPINN), yielding a fully quantum feature map. Our findings emphasize the critical role of embedding design and support hybrid quantum-classical approaches for parabolic PDE modeling in the NISQ era.

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